Preheat the oven to 350°F. Grease a 9x13-inch pan.
In a small bowl, mix brown sugar and cinnamon. Set aside.
In a large bowl, whisk together cake mix, eggs, sour cream, butter, vegetable oil, water and extracts until smooth.
Pour half of the batter into the prepared pan. Sprinkle the brown sugar mixture over the batter, then dollop the remaining batter on top. Using a knife, insert it half ways into the batter and swirl back and forth along the cake.
Bake for 32-35 minutes, or until lightly golden brown (a toothpick inserted in the middle should come out clean).
While cake is baking, make icing in a medium bowl by whisking together the powdered sugar, half and half and vanilla extract until smooth.
Pour the icing over the cake while warm and allow to cool before cutting and serving.